You're laboring with some very basic misunderstandings about sharpening. I'm not saying you can't sharpen a perfectly good edge without being able to conceptualize the geometries and the process, but some degree of understanding is a big help to most people.
Get yourself some graph paper and/or a protractor and draw yourself some huge angles. Do multiple pictures and set them around your sharpening area so your eyes help but light on one. You can use those to compare your knife angles -- close enough. As a bonus, your wife will think you're nuts.
With a "V" edge -- which is the type of edge you're sharpening -- it's almost always to sharpen both sides to the same angle(s). If for no other reason than it makes steeling and re-sharpening easier. But it also makes for a stronger edge. Sharpening to equal angles is true for all but the most asymmetric of edges.
The sharpness of your edge has very little to do with the angles. You can sharpen a very, very sharp edge to very obtuse angles. By way of example, shaving with an axe or a cleaver is a trick a lot of sharpeners use to showcase their skills. My "chef de chef" (a 12" carbon Sab) is sharpened to a 20* over 25* double bevel and when it's fresh off the stones will cut through chicken wings by accident -- that is, just resting the knife on the bird and answering the phone. That's not only pretty darn sharp, I daresay it's sharper than any knife you've ever used. The point being not only are there other aspects besides angles, but that the angles themselves aren't even that important. My feeling is that you're overemphasizing them.
You want your edge angles to be as acute as your knife will hold -- but no more acute than that. Err on the side of obtuseness or you'll be using your steel every time you use your knife. In other words, too often. When you're trying to sharpen the "best" edge, there's always some tension between absolute sharpness and durability. Try not to tip too far over to one side. Your Globals do fine at 15*, your Germans at 20* and that's just hunky-dory. Don't try to turn a Henckels into a Tadatsuna. They aren't built to be the same and you can't make it so on the stones. For that matter, you can't make a Global act like a Tadatsuna. Although Globals are made and designed and Japan, as a result of their width and alloy they act as much like German made knives as Japanese. If you're want a knife that performs like one of the Japanese "lasers," I'm afraid you'll need to buy one.
As I wrote earlier if you want to optimize the performance you can try a double bevel -- but for most knives that represents a lot of work for a smallish improvement. But as long as you're not too aggressive about thinning, you're not going to hurt anything by trying. Also, at the risk of setting the cart before the horse, you can make the double bevel process more efficient by "micro-beveling" the primary (cutting) edge angle. If you were doing 20/15 for instance, that would mean sharpening the edge to 15* going all the way through your stone set, then using your fine stones only for a few strokes to sharpen and polish the 20*. It's not quite as durable as a true double bevel, but will stand up quite a bit longer than using an edge that's otherwise too acute.
I have the feeling that you still don't get that you can't sharpen a 15* angle over a 20* angle without completely re-profiling the knife. If you try you'll only sharpen the top of the bevel without the cutting edge ever touching the stone. You might need to try the "Magic Maker trick" just to get some idea of how angles work. If you haven't already tried it, now is a great time to start.
Hope this helps,